Multiple choice

Let $E, F$ and $G$ be finite sets. Let

$X = (E ∩ F) - (F ∩ G)$ and $Y = (E - (E ∩ G)) - (E - F)$.

Which one of the following is true?

  1. $X ⊂ Y$
  2. $X ⊃ Y$
  3. $X = Y$
  4. $X - Y ≠ \phi$ and $Y - X ≠ \phi$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

X = (E ∩ F) - (F ∩ G) = elements in E and F but not in G. Y = (E - (E ∩ G)) - (E - F) = elements in E that are not exclusively in E (not in G) and are in F. Simplifying Y: elements in E that are in F but not in G. Therefore X = Y. Both represent elements that are in E and F but not in G.

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